# MATU9M1 - Mathematics I

SCQF Level: 8
Availability: Semester module, Autumn
Course Prerequisite: Either Higher or A level Mathematics
Credit Value: 20 (1 module)

### Aims

To develop skills in solving linear simultaneous equations; to use matrix theory to understand the nature of their solutions; to apply vector and matrix techniques in studying the geometry of lines and planes.
To review, consolidate and develop understanding of the differential and integral calculus; to use the calculus to solve a range of "real-world" problems.
Complex numbers will also be studied, and used to provide a link between the exponential and trigonometric functions.

### Learning Outcomes

Students should be able to solve a system of linear equations; solve geometrical problems of lines and planes; describe a discrete dynamical system; carry out calculations with complex numbers; differentiate elementary functions involving algebraic, trigonometric, exponential and logarithmic functions; integrate using standard techniques such as partial fractions, parts and substitution; and apply calculus methods to optimisation problems. Students should also be able to demonstrate the ability to apply theory and techniques to unseen problems without reference to notes, to work independently and under a time constraint.

### Content

A1: Complex numbers: Argand plane representation, polar form.
A2: Linear simultaneous equations: row echelon form, applications.
A3: The geometry of lines and planes.
A4: A matrix treatment of linear simultaneous equations: determinants, eigenvalues and eigenvectors.

B1: Functions and inverse functions.
B2: The differential calculus, rules of differentiation;optimisation.
B3: Exponential and logarithmic functions
B4: The integral calculus, rules of integration.

### Transferable Skills

Methodical working, problem solving.

### Bibliography

R.A. ADAMS, "Calculus: A Complete Course", Pearson
H. ANTON and C. RORRES, "Elementary Linear Algebra with Applications", Wiley
F. AYRES and E. MENDELSON, "Calculus", (Schaum's Easy Outline Series) McGraw-Hill
L. ALCOCK, "How to Study for a Mathematics Degree", Oxford University Press

### Teaching Format

4 one-hour lectures and a 1.5 hour tutorial per week.

### Assessment

40% coursework (including 2 class tests) and 60% examination

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